Question

George hiked from the top of a hill to the valley floor. The elevation at the top of the hill is 127 feet above sea level. The valley floor is 52 feet below sea level. George stopped at a rest stop that is at an elevation exactly halfway between the top of the hill and the valley floor. What is the elevation, in feet, of the rest stop? Show your work

Answer 1

Answer:

The elevation of the rest stop is 37.5 feet above sea level.

Step-by-step explanation:

Given that the elevation at the top of the hill is 127 feet above sea level and The valley floor is 52 feet below sea level.

So, the total length from the top of the hill to the valley floor

$l= 127+52 = 179$ feet

So, length of halfway $= l/2=179/2=89.5$ feet ...(i)

Assuming that the stop for rest, the halfway between the top of the hill and the valley floor, is at x feet above sea level.

So, the length between the stop position and the valley floor $= 52 +x$ feet.

As the stop position is at half-way, so by using equation (i), we have,

$52 + x = 89.5 \\\\\Rightarrow x =89.5-52$

$\Rightarrow x=37.5$ feet

Hence, the elevation of the rest stop is 37.5 feet above sea level.